This paper describes a technique for gray image noise cancellation. This method
employs linear matrix inequality (LMI) and particle swarm optimization (PSO) based on
cellular neural networks (CNN).We use two images that one is desired image and the other is corrupted to find the CNN template. The Lyapunov stability theorem is employed to derive the criterion for uniqueness and global asymptotic stability of the CNN equilibrium point.The current study characterizes the template design problem as a standard LMI problem and
the optimization parameters of the templates are carried out by PSO. Finally, the examples
are given to illustrate the effectiveness of the proposed method.